Below is the diamgram of the region.Originally Posted by JaysFan31
In order to solve this problem you need to find the countinous density function. Which you say is proportional to the distance. I take this to mean that you are saying directly proportional right? Then you have,
for some constant of proportionality.
In mathematical terms,
In order to find the center of mass you first need to find the mass. Which in this case is,
I believe it is easier by converting to polar cordinates.
I will continue later.